Each sensor uses a local Kalman filter (KF) to pre-process its measurement before sending to the gateway [1]}.
We have
\(\mathbf {x}^s_n ({t|t-1})&=\mathbf {A}_n \mathbf {x}^s_n ({t-1})\\\mathbf {P}^s_n ({t|t-1})&=\mathbf {A}_n \mathbf {P}^s_n ({t-1}) \mathbf {A}^{\top }_n+\mathbf {W}_n\\\mathbf {K}_n (t)&=\mathbf {P}^s_n ({t|t-1}) \mathbf {C}^{\top }_n(\mathbf {C}_n \mathbf {P}^s_n ({t|t-1}) \mathbf {C}^{\top }_n+\mathbf {Z}_n)^{-1}\\\mathbf {x}^s_n (t)&=\mathbf {x}^s_n ({t|t-1})+\mathbf {K}_n (t)(\mathbf {y}_n({t})-\mathbf {C}_n \mathbf {x}^s_n ({t|t-1}))\\\mathbf {P}^s_n (t)&=(\mathbf {I}_n-\mathbf {K}_n ({t}) \mathbf {C}_n)\mathbf {P}^s_n ({t|t-1})\) 
